Publikation: Evolution of convex lens-shaped networks under the curve shortening flow
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2011
Autor:innen
Azouani, Abderrahim
Georgi, Marc
Hell, Juliette
Jangle, Nihar
Koeller, Amos
Marxen, Tobias
Ritthaler, Sandra
Sáez, Mariel
Schulze, Felix
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Transactions of the American Mathematical Society. 2011, 363(5), pp. 2265-2294
Zusammenfassung
We consider convex symmetric lens-shaped networks in R2 that evolve under the curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.
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510 Mathematik
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SCHNÜRER, Oliver C., Abderrahim AZOUANI, Marc GEORGI, Juliette HELL, Nihar JANGLE, Amos KOELLER, Tobias MARXEN, Sandra RITTHALER, Mariel SÁEZ, Felix SCHULZE, Brian SMITH, 2011. Evolution of convex lens-shaped networks under the curve shortening flow. In: Transactions of the American Mathematical Society. 2011, 363(5), pp. 2265-2294BibTex
@article{Schnurer2011Evolu-19149,
year={2011},
title={Evolution of convex lens-shaped networks under the curve shortening flow},
number={5},
volume={363},
journal={Transactions of the American Mathematical Society},
pages={2265--2294},
author={Schnürer, Oliver C. and Azouani, Abderrahim and Georgi, Marc and Hell, Juliette and Jangle, Nihar and Koeller, Amos and Marxen, Tobias and Ritthaler, Sandra and Sáez, Mariel and Schulze, Felix and Smith, Brian}
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<dcterms:abstract xml:lang="eng">We consider convex symmetric lens-shaped networks in R2 that evolve under the curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.</dcterms:abstract>
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